Why air displacement is what counts. At low frequencies sound pressure is proportional to how much air the cone pushes in one stroke: area × excursion. That is why a long-excursion 12 can easily beat a short-excursion 15. The decibel difference is 20 · log10(displacement ratio) : twice the air is 6 dB.
Area is not the nominal size. The moving area (Sd) of a 12-inch sub is roughly 25 cm across, not 30 — the basket and surround do not move. The values here are typical; if the spec sheet lists Sd, use that, because it varies by manufacturer.
What this does not tell you. How much power it takes to reach full excursion, how big an enclosure it needs, or whether the sub can take the heat. Two subs need twice the space and usually twice the amplifier — the result shows what a setup is capable of, not whether it is cheaper.